{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.HMM实践\n",
    "\n",
    "我们使用hmmlearn实践一下。详细参见[官方文档](https://hmmlearn.readthedocs.io/en/latest/)：https://hmmlearn.readthedocs.io/en/latest/\n",
    "\n",
    "hmmlearn实现了三种HMM模型类，按照观测状态是连续状态还是离散状态，可以分为两类。GaussianHMM和GMMHMM是连续观测状态的HMM模型，而MultinomialHMM是离散观测状态的模型，也是我们在HMM原理系列篇里面使用的模型。\n",
    "\n",
    "以下是使用HMM进行采样的例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\23361\\AppData\\Local\\Temp/ipykernel_13432/3509860873.py:47: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  fig.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#pip install hmmlearn\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from hmmlearn import hmm\n",
    "\n",
    "# Prepare parameters for a 4-components HMM\n",
    "# Initial population probability\n",
    "startprob = np.array([0.6, 0.3, 0.1, 0.0])\n",
    "# The transition matrix, note that there are no transitions possible\n",
    "# between component 1 and 3\n",
    "transmat = np.array([[0.7, 0.2, 0.0, 0.1],\n",
    "                     [0.3, 0.5, 0.2, 0.0],\n",
    "                     [0.0, 0.3, 0.5, 0.2],\n",
    "                     [0.2, 0.0, 0.2, 0.6]])\n",
    "# The means of each component\n",
    "means = np.array([[0.0, 0.0],\n",
    "                  [0.0, 11.0],\n",
    "                  [9.0, 10.0],\n",
    "                  [11.0, -1.0]])\n",
    "# The covariance of each component\n",
    "covars = .5 * np.tile(np.identity(2), (4, 1, 1))\n",
    "\n",
    "# Build an HMM instance and set parameters\n",
    "gen_model = hmm.GaussianHMM(n_components=4, covariance_type=\"full\")\n",
    "\n",
    "# Instead of fitting it from the data, we directly set the estimated\n",
    "# parameters, the means and covariance of the components\n",
    "gen_model.startprob_ = startprob\n",
    "gen_model.transmat_ = transmat\n",
    "gen_model.means_ = means\n",
    "gen_model.covars_ = covars\n",
    "\n",
    "# Generate samples\n",
    "X, Z = gen_model.sample(500)\n",
    "\n",
    "# Plot the sampled data\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(X[:, 0], X[:, 1], \".-\", label=\"observations\", ms=6,\n",
    "        mfc=\"orange\", alpha=0.7)\n",
    "\n",
    "# Indicate the component numbers\n",
    "for i, m in enumerate(means):\n",
    "    ax.text(m[0], m[1], 'Component %i' % (i + 1),\n",
    "            size=17, horizontalalignment='center',\n",
    "            bbox=dict(alpha=.7, facecolor='w'))\n",
    "ax.legend(loc='best')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged: True\tScore: -1065.5259488089373\n",
      "Converged: True\tScore: -904.2908933008515\n",
      "Converged: True\tScore: -905.5449538166446\n",
      "The best model had a score of -904.2908933008515 and 4 states\n"
     ]
    }
   ],
   "source": [
    "scores = list()\n",
    "models = list()\n",
    "for n_components in (3, 4, 5):\n",
    "    # define our hidden Markov model\n",
    "    model = hmm.GaussianHMM(n_components=n_components,\n",
    "                            covariance_type='full', n_iter=10)\n",
    "    model.fit(X[:X.shape[0] // 2])  # 50/50 train/validate\n",
    "    models.append(model)\n",
    "    scores.append(model.score(X[X.shape[0] // 2:]))\n",
    "    print(f'Converged: {model.monitor_.converged}'\n",
    "          f'\\tScore: {scores[-1]}')\n",
    "\n",
    "# get the best model\n",
    "model = models[np.argmax(scores)]\n",
    "n_states = model.n_components\n",
    "print(f'The best model had a score of {max(scores)} and {n_states} '\n",
    "      'states')\n",
    "\n",
    "# use the Viterbi algorithm to predict the most likely sequence of states\n",
    "# given the model\n",
    "states = model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\23361\\AppData\\Local\\Temp/ipykernel_13432/3700403680.py:8: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  fig.show()\n",
      "C:\\Users\\23361\\AppData\\Local\\Temp/ipykernel_13432/3700403680.py:21: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  fig.show()\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#让我们将我们的状态与生成的状态和我们的转换矩阵进行比较，来看我们的模型\n",
    "# plot model states over time\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(Z, states)\n",
    "ax.set_title('States compared to generated')\n",
    "ax.set_xlabel('Generated State')\n",
    "ax.set_ylabel('Recovered State')\n",
    "fig.show()\n",
    "\n",
    "# plot the transition matrix\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 5))\n",
    "ax1.imshow(gen_model.transmat_, aspect='auto', cmap='spring')\n",
    "ax1.set_title('Generated Transition Matrix')\n",
    "ax2.imshow(model.transmat_, aspect='auto', cmap='spring')\n",
    "ax2.set_title('Recovered Transition Matrix')\n",
    "for ax in (ax1, ax2):\n",
    "    ax.set_xlabel('State To')\n",
    "    ax.set_ylabel('State From')\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "5f04dd1d6b72ff9d002f9c97d3bf130820120c0ac9ec7321437503cd785f0e6e"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
